src/HOL/Auth/Yahalom.ML

 
 (*Weak liveness: there are traces that reach the end*)
 
 goal thy 
  "!!A B. [| A ~= B; A ~= Server; B ~= Server |]   \
-\        ==> EX X NB K. EX evs: yahalom.          \
+\        ==> EX X NB K. EX evs: yahalom lost.          \
 \               Says A B {|X, Crypt (Nonce NB) K|} : set_of_list evs";
 by (REPEAT (resolve_tac [exI,bexI] 1));
-br (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS yahalom.YM4) 2;
+by (rtac (yahalom.Nil RS yahalom.YM1 RS yahalom.YM2 RS yahalom.YM3 RS yahalom.YM4) 2);
 by (ALLGOALS (simp_tac (!simpset setsolver safe_solver)));
 by (ALLGOALS Fast_tac);
 result();
 
 
 (**** Inductive proofs about yahalom ****)
 
-(*The Enemy can see more than anybody else, except for their initial state*)
-goal thy 
- "!!evs. evs : yahalom ==> \
-\     sees A evs <= initState A Un sees Enemy evs";
-be yahalom.induct 1;
+(*The Spy can see more than anybody else, except for their initial state*)
+goal thy 
+ "!!evs. evs : yahalom lost ==> \
+\     sees lost A evs <= initState lost A Un sees lost Spy evs";
+by (etac yahalom.induct 1);
 by (ALLGOALS (fast_tac (!claset addDs [sees_Says_subset_insert RS subsetD] 
-			        addss (!simpset))));
-qed "sees_agent_subset_sees_Enemy";
+                                addss (!simpset))));
+qed "sees_agent_subset_sees_Spy";
 
 
 (*Nobody sends themselves messages*)
-goal thy "!!evs. evs : yahalom ==> ALL A X. Says A A X ~: set_of_list evs";
-be yahalom.induct 1;
+goal thy "!!evs. evs : yahalom lost ==> ALL A X. Says A A X ~: set_of_list evs";
+by (etac yahalom.induct 1);
 by (Auto_tac());
 qed_spec_mp "not_Says_to_self";
 Addsimps [not_Says_to_self];
 AddSEs   [not_Says_to_self RSN (2, rev_notE)];
 
 
 (** For reasoning about the encrypted portion of messages **)
 
 (*Lets us treat YM4 using a similar argument as for the Fake case.*)
 goal thy "!!evs. Says S A {|Crypt Y (shrK A), X|} : set_of_list evs ==> \
-\                X : analz (sees Enemy evs)";
-by (fast_tac (!claset addSDs [Says_imp_sees_Enemy RS analz.Inj]) 1);
-qed "YM4_analz_sees_Enemy";
+\                X : analz (sees lost Spy evs)";
+by (fast_tac (!claset addSDs [Says_imp_sees_Spy RS analz.Inj]) 1);
+qed "YM4_analz_sees_Spy";
 
 goal thy "!!evs. Says S A {|Crypt {|B, K, NA, NB|} (shrK A), X|} \
 \                  : set_of_list evs ==> \
-\                K : parts (sees Enemy evs)";
+\                K : parts (sees lost Spy evs)";
 by (fast_tac (!claset addSEs partsEs
-	              addSDs [Says_imp_sees_Enemy RS parts.Inj]) 1);
-qed "YM4_parts_sees_Enemy";
-
-
-
-(** Theorems of the form X ~: parts (sees Enemy evs) imply that NOBODY
+                      addSDs [Says_imp_sees_Spy RS parts.Inj]) 1);
+qed "YM4_parts_sees_Spy";
+
+
+
+(** Theorems of the form X ~: parts (sees lost Spy evs) imply that NOBODY
     sends messages containing X! **)
 
-(*Enemy never sees another agent's shared key! (unless it is leaked at start)*)
-goal thy 
- "!!evs. [| evs : yahalom;  A ~: bad |]    \
-\        ==> Key (shrK A) ~: parts (sees Enemy evs)";
-be yahalom.induct 1;
-bd (YM4_analz_sees_Enemy RS synth.Inj) 6;
+(*Spy never sees lost another agent's shared key! (unless it is leaked at start)*)
+goal thy 
+ "!!evs. [| evs : yahalom lost;  A ~: lost |]    \
+\        ==> Key (shrK A) ~: parts (sees lost Spy evs)";
+by (etac yahalom.induct 1);
+by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6);
 by (ALLGOALS Asm_simp_tac);
 by (stac insert_commute 3);
 by (Auto_tac());
 (*Fake and YM4 are similar*)
 by (ALLGOALS (best_tac (!claset addSDs [impOfSubs analz_subset_parts,
-					impOfSubs Fake_parts_insert])));
-qed "Enemy_not_see_shrK";
-
-bind_thm ("Enemy_not_analz_shrK",
-	  [analz_subset_parts, Enemy_not_see_shrK] MRS contra_subsetD);
-
-Addsimps [Enemy_not_see_shrK, Enemy_not_analz_shrK];
+                                        impOfSubs Fake_parts_insert])));
+qed "Spy_not_see_shrK";
+
+bind_thm ("Spy_not_analz_shrK",
+          [analz_subset_parts, Spy_not_see_shrK] MRS contra_subsetD);
+
+Addsimps [Spy_not_see_shrK, Spy_not_analz_shrK];
 
 (*We go to some trouble to preserve R in the 3rd and 4th subgoals
   As usual fast_tac cannot be used because it uses the equalities too soon*)
 val major::prems = 
-goal thy  "[| Key (shrK A) : parts (sees Enemy evs);       \
-\             evs : yahalom;                               \
-\             A:bad ==> R                                  \
+goal thy  "[| Key (shrK A) : parts (sees lost Spy evs);       \
+\             evs : yahalom lost;                               \
+\             A:lost ==> R                                  \
 \           |] ==> R";
-br ccontr 1;
-br ([major, Enemy_not_see_shrK] MRS rev_notE) 1;
+by (rtac ccontr 1);
+by (rtac ([major, Spy_not_see_shrK] MRS rev_notE) 1);
 by (swap_res_tac prems 2);
 by (ALLGOALS (fast_tac (!claset addIs prems)));
-qed "Enemy_see_shrK_E";
-
-bind_thm ("Enemy_analz_shrK_E", 
-	  analz_subset_parts RS subsetD RS Enemy_see_shrK_E);
-
-AddSEs [Enemy_see_shrK_E, Enemy_analz_shrK_E];
+qed "Spy_see_shrK_E";
+
+bind_thm ("Spy_analz_shrK_E", 
+          analz_subset_parts RS subsetD RS Spy_see_shrK_E);
+
+AddSEs [Spy_see_shrK_E, Spy_analz_shrK_E];
 
 
 (*** Future keys can't be seen or used! ***)
 
 (*Nobody can have SEEN keys that will be generated in the future.
   This has to be proved anew for each protocol description,
   but should go by similar reasoning every time.  Hardest case is the
   standard Fake rule.  
       The length comparison, and Union over C, are essential for the 
   induction! *)
-goal thy "!!evs. evs : yahalom ==> \
+goal thy "!!evs. evs : yahalom lost ==> \
 \                length evs <= length evs' --> \
-\                          Key (newK evs') ~: (UN C. parts (sees C evs))";
-be yahalom.induct 1;
-bd (YM4_analz_sees_Enemy RS synth.Inj) 6;
+\                          Key (newK evs') ~: (UN C. parts (sees lost C evs))";
+by (etac yahalom.induct 1);
+by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6);
 by (REPEAT_FIRST (best_tac (!claset addDs [impOfSubs analz_subset_parts,
-					   impOfSubs parts_insert_subset_Un,
-					   Suc_leD]
-			            addss (!simpset))));
+                                           impOfSubs parts_insert_subset_Un,
+                                           Suc_leD]
+                                    addss (!simpset))));
 val lemma = result();
 
 (*Variant needed for the main theorem below*)
 goal thy 
- "!!evs. [| evs : yahalom;  length evs <= length evs' |]    \
-\        ==> Key (newK evs') ~: parts (sees C evs)";
+ "!!evs. [| evs : yahalom lost;  length evs <= length evs' |]    \
+\        ==> Key (newK evs') ~: parts (sees lost C evs)";
 by (fast_tac (!claset addDs [lemma]) 1);
 qed "new_keys_not_seen";
 Addsimps [new_keys_not_seen];
 
 (*Another variant: old messages must contain old keys!*)
 goal thy 
  "!!evs. [| Says A B X : set_of_list evs;  \
 \           Key (newK evt) : parts {X};    \
-\           evs : yahalom                 \
+\           evs : yahalom lost                 \
 \        |] ==> length evt < length evs";
-br ccontr 1;
-bd leI 1;
-by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Enemy]
+by (rtac ccontr 1);
+by (dtac leI 1);
+by (fast_tac (!claset addSDs [new_keys_not_seen, Says_imp_sees_Spy]
                       addIs  [impOfSubs parts_mono]) 1);
 qed "Says_imp_old_keys";
 
 
 (*Nobody can have USED keys that will be generated in the future.
   ...very like new_keys_not_seen*)
-goal thy "!!evs. evs : yahalom ==> \
+goal thy "!!evs. evs : yahalom lost ==> \
 \                length evs <= length evs' --> \
-\                newK evs' ~: keysFor (UN C. parts (sees C evs))";
-be yahalom.induct 1;
-by (forward_tac [YM4_parts_sees_Enemy] 6);
-bd (YM4_analz_sees_Enemy RS synth.Inj) 6;
+\                newK evs' ~: keysFor (UN C. parts (sees lost C evs))";
+by (etac yahalom.induct 1);
+by (forward_tac [YM4_parts_sees_Spy] 6);
+by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6);
 by (ALLGOALS Asm_full_simp_tac);
 (*YM1, YM2 and YM3*)
 by (EVERY (map (fast_tac (!claset addDs [Suc_leD] addss (!simpset))) [4,3,2]));
 (*Fake and YM4: these messages send unknown (X) components*)
 by (stac insert_commute 2);

 (*YM4: the only way K could have been used is if it had been seen,
   contradicting new_keys_not_seen*)
 by (ALLGOALS
      (best_tac
       (!claset addDs [impOfSubs analz_subset_parts,
-		      impOfSubs (analz_subset_parts RS keysFor_mono),
-		      impOfSubs (parts_insert_subset_Un RS keysFor_mono),
-		      Suc_leD]
-	       addEs [new_keys_not_seen RSN(2,rev_notE)]
-	       addss (!simpset))));
+                      impOfSubs (analz_subset_parts RS keysFor_mono),
+                      impOfSubs (parts_insert_subset_Un RS keysFor_mono),
+                      Suc_leD]
+               addEs [new_keys_not_seen RSN(2,rev_notE)]
+               addss (!simpset))));
 val lemma = result();
 
 goal thy 
- "!!evs. [| evs : yahalom;  length evs <= length evs' |]    \
-\        ==> newK evs' ~: keysFor (parts (sees C evs))";
+ "!!evs. [| evs : yahalom lost;  length evs <= length evs' |]    \
+\        ==> newK evs' ~: keysFor (parts (sees lost C evs))";
 by (fast_tac (!claset addSDs [lemma] addss (!simpset)) 1);
 qed "new_keys_not_used";
 
 bind_thm ("new_keys_not_analzd",
-	  [analz_subset_parts RS keysFor_mono,
-	   new_keys_not_used] MRS contra_subsetD);
+          [analz_subset_parts RS keysFor_mono,
+           new_keys_not_used] MRS contra_subsetD);
 
 Addsimps [new_keys_not_used, new_keys_not_analzd];
 
 
 (** Lemmas concerning the form of items passed in messages **)
 
 
 (****
  The following is to prove theorems of the form
 
-          Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) ==>
-          Key K : analz (sees Enemy evs)
+          Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) ==>
+          Key K : analz (sees lost Spy evs)
 
  A more general formula must be proved inductively.
 
 ****)
 
 
 (*NOT useful in this form, but it says that session keys are not used
   to encrypt messages containing other keys, in the actual protocol.
   We require that agents should behave like this subsequently also.*)
 goal thy 
- "!!evs. evs : yahalom ==> \
-\        (Crypt X (newK evt)) : parts (sees Enemy evs) & \
-\        Key K : parts {X} --> Key K : parts (sees Enemy evs)";
-be yahalom.induct 1;
-bd (YM4_analz_sees_Enemy RS synth.Inj) 6;
+ "!!evs. evs : yahalom lost ==> \
+\        (Crypt X (newK evt)) : parts (sees lost Spy evs) & \
+\        Key K : parts {X} --> Key K : parts (sees lost Spy evs)";
+by (etac yahalom.induct 1);
+by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6);
 by (ALLGOALS (asm_simp_tac (!simpset addsimps pushes)));
 (*Deals with Faked messages*)
 by (EVERY 
     (map (best_tac (!claset addSEs partsEs
-			    addDs [impOfSubs parts_insert_subset_Un]
-			    addss (!simpset)))
+                            addDs [impOfSubs parts_insert_subset_Un]
+                            addss (!simpset)))
      [3,2]));
 (*Base case*)
 by (Auto_tac());
 result();
 

 Addsimps [image_insert RS sym];
 
 Delsimps [image_Un];
 Addsimps [image_Un RS sym];
 
-goal thy "insert (Key (newK x)) (sees A evs) = \
-\         Key `` (newK``{x}) Un (sees A evs)";
+goal thy "insert (Key (newK x)) (sees lost A evs) = \
+\         Key `` (newK``{x}) Un (sees lost A evs)";
 by (Fast_tac 1);
 val insert_Key_singleton = result();
 
 goal thy "insert (Key (f x)) (Key``(f``E) Un C) = \
 \         Key `` (f `` (insert x E)) Un C";

 val insert_Key_image = result();
 
 
 (*This lets us avoid analyzing the new message -- unless we have to!*)
 (*NEEDED??*)
-goal thy "synth (analz (sees Enemy evs)) <=   \
-\         synth (analz (sees Enemy (Says A B X # evs)))";
+goal thy "synth (analz (sees lost Spy evs)) <=   \
+\         synth (analz (sees lost Spy (Says A B X # evs)))";
 by (Simp_tac 1);
-br (subset_insertI RS analz_mono RS synth_mono) 1;
+by (rtac (subset_insertI RS analz_mono RS synth_mono) 1);
 qed "synth_analz_thin";
 
 AddIs [impOfSubs synth_analz_thin];
 
 

 by (fast_tac (!claset addSEs [impOfSubs analz_mono]) 1);
 val lemma = result();
 
 
 goal thy  
- "!!evs. evs : yahalom ==> \
-\  ALL K E. (Key K : analz (Key``(newK``E) Un (sees Enemy evs))) = \
-\           (K : newK``E | Key K : analz (sees Enemy evs))";
-be yahalom.induct 1;
-bd YM4_analz_sees_Enemy 6;
+ "!!evs. evs : yahalom lost ==> \
+\  ALL K E. (Key K : analz (Key``(newK``E) Un (sees lost Spy evs))) = \
+\           (K : newK``E | Key K : analz (sees lost Spy evs))";
+by (etac yahalom.induct 1);
+by (dtac YM4_analz_sees_Spy 6);
 by (REPEAT_FIRST (resolve_tac [allI, lemma]));
 by (ALLGOALS 
     (asm_simp_tac 
      (!simpset addsimps ([insert_Key_singleton, insert_Key_image, pushKey_newK]
-			 @ pushes)
+                         @ pushes)
                setloop split_tac [expand_if])));
 (*YM4*) 
-by (enemy_analz_tac 4);
+by (spy_analz_tac 4);
 (*YM3*)
 by (Fast_tac 3);
 (*Fake case*)
-by (enemy_analz_tac 2);
+by (spy_analz_tac 2);
 (*Base case*)
 by (fast_tac (!claset addIs [image_eqI] addss (!simpset)) 1);
 qed_spec_mp "analz_image_newK";
 
 goal thy
- "!!evs. evs : yahalom ==>                               \
-\        Key K : analz (insert (Key (newK evt)) (sees Enemy evs)) = \
-\        (K = newK evt | Key K : analz (sees Enemy evs))";
+ "!!evs. evs : yahalom lost ==>                               \
+\        Key K : analz (insert (Key (newK evt)) (sees lost Spy evs)) = \
+\        (K = newK evt | Key K : analz (sees lost Spy evs))";
 by (asm_simp_tac (HOL_ss addsimps [pushKey_newK, analz_image_newK, 
-				   insert_Key_singleton]) 1);
+                                   insert_Key_singleton]) 1);
 by (Fast_tac 1);
 qed "analz_insert_Key_newK";
 
 
 (*Describes the form of K when the Server sends this message.*)
 goal thy 
  "!!evs. [| Says Server A                                           \
 \            {|Crypt {|Agent B, K, NA, NB|} (shrK A),               \
 \              Crypt {|Agent A, K|} (shrK B)|} : set_of_list evs;   \
-\           evs : yahalom |]                                        \
-\        ==> (EX evt:yahalom. K = Key(newK evt))";
-be rev_mp 1;
-be yahalom.induct 1;
+\           evs : yahalom lost |]                                        \
+\        ==> (EX evt: yahalom lost. K = Key(newK evt))";
+by (etac rev_mp 1);
+by (etac yahalom.induct 1);
 by (ALLGOALS (fast_tac (!claset addss (!simpset))));
 qed "Says_Server_message_form";
 
 
-(** Crucial secrecy property: Enemy does not see the keys sent in msg YM3
+(** Crucial secrecy property: Spy does not see the keys sent in msg YM3
     As with Otway-Rees, proof does not need uniqueness of session keys. **)
 
 goal thy 
- "!!evs. [| A ~: bad;  B ~: bad;  evs : yahalom;  evt : yahalom |]        \
+ "!!evs. [| A ~: lost;  B ~: lost;  evs : yahalom lost;  evt : yahalom lost |]        \
 \        ==> Says Server A                                                \
 \              {|Crypt {|Agent B, Key(newK evt), NA, NB|} (shrK A),       \
 \                Crypt {|Agent A, Key(newK evt)|} (shrK B)|}              \
 \             : set_of_list evs -->    \
-\            Key(newK evt) ~: analz (sees Enemy evs)";
-be yahalom.induct 1;
-bd YM4_analz_sees_Enemy 6;
+\            Key(newK evt) ~: analz (sees lost Spy evs)";
+by (etac yahalom.induct 1);
+by (dtac YM4_analz_sees_Spy 6);
 by (ALLGOALS
     (asm_simp_tac 
      (!simpset addsimps ([analz_subset_parts RS contra_subsetD,
-			  analz_insert_Key_newK] @ pushes)
+                          analz_insert_Key_newK] @ pushes)
                setloop split_tac [expand_if])));
 (*YM4*)
-by (enemy_analz_tac 3);
+by (spy_analz_tac 3);
 (*YM3*)
 by (fast_tac (!claset addIs [parts_insertI]
-		      addEs [Says_imp_old_keys RS less_irrefl]
-	              addss (!simpset)) 2);
+                      addEs [Says_imp_old_keys RS less_irrefl]
+                      addss (!simpset)) 2);
 (*Fake*) (** LEVEL 10 **)
-by (enemy_analz_tac 1);
+by (spy_analz_tac 1);
 val lemma = result() RS mp RSN(2,rev_notE);
 
 
 (*Final version: Server's message in the most abstract form*)
 goal thy 
  "!!evs. [| Says Server A \
 \            {|Crypt {|Agent B, K, NA, NB|} (shrK A),                   \
 \              Crypt {|Agent A, K|} (shrK B)|} : set_of_list evs;       \
-\           A ~: bad;  B ~: bad;  evs : yahalom |] ==>                  \
-\     K ~: analz (sees Enemy evs)";
+\           A ~: lost;  B ~: lost;  evs : yahalom lost |] ==>                  \
+\     K ~: analz (sees lost Spy evs)";
 by (forward_tac [Says_Server_message_form] 1 THEN assume_tac 1);
 by (fast_tac (!claset addSEs [lemma]) 1);
-qed "Enemy_not_see_encrypted_key";
+qed "Spy_not_see_encrypted_key";
 
 
 (** Towards proofs of stronger authenticity properties **)
 
 goal thy 
- "!!evs. [| Crypt {|Agent A, Key K|} (shrK B) : parts (sees Enemy evs); \
-\           B ~: bad;  evs : yahalom |]                                 \
+ "!!evs. [| Crypt {|Agent A, Key K|} (shrK B) : parts (sees lost Spy evs); \
+\           B ~: lost;  evs : yahalom lost |]                                 \
 \        ==> EX NA NB. Says Server A                                    \
 \                        {|Crypt {|Agent B, Key K,                      \
 \                                  Nonce NA, Nonce NB|} (shrK A),       \
 \                          Crypt {|Agent A, Key K|} (shrK B)|}          \
 \                       : set_of_list evs";
-be rev_mp 1;
-be yahalom.induct 1;
-bd (YM4_analz_sees_Enemy RS synth.Inj) 6;
+by (etac rev_mp 1);
+by (etac yahalom.induct 1);
+by (dtac (YM4_analz_sees_Spy RS synth.Inj) 6);
 by (ALLGOALS Asm_simp_tac);
 (*YM3*)
 by (Fast_tac 3);
 (*Base case*)
 by (fast_tac (!claset addss (!simpset)) 1);
 (*Prepare YM4*)
 by (stac insert_commute 2 THEN Simp_tac 2);
 (*Fake and YM4 are similar*)
 by (ALLGOALS (best_tac (!claset addSDs [impOfSubs analz_subset_parts,
-					impOfSubs Fake_parts_insert])));
+                                        impOfSubs Fake_parts_insert])));
 qed "Crypt_imp_Server_msg";
 
 
 (*What can B deduce from receipt of YM4?  
   NOT THAT THE NONCES AGREE (in this version).  But what does the Nonce
-	give us??*)
+        give us??*)
 goal thy 
  "!!evs. [| Says A' B {|Crypt {|Agent A, Key K|} (shrK B),              \
 \                       Crypt (Nonce NB) K|} : set_of_list evs;         \
-\           B ~: bad;  evs : yahalom |]                                 \
+\           B ~: lost;  evs : yahalom lost |]                                 \
 \        ==> EX NA NB. Says Server A                                    \
 \                     {|Crypt {|Agent B, Key K,                         \
 \                               Nonce NA, Nonce NB|} (shrK A),          \
 \                       Crypt {|Agent A, Key K|} (shrK B)|}             \
 \                   : set_of_list evs";
-be rev_mp 1;
-be yahalom.induct 1;
-by (dresolve_tac [YM4_analz_sees_Enemy] 6);
+by (etac rev_mp 1);
+by (etac yahalom.induct 1);
+by (dtac YM4_analz_sees_Spy 6);
 by (ALLGOALS Asm_simp_tac);
 by (ALLGOALS (fast_tac (!claset addSDs [impOfSubs analz_subset_parts RS
-					Crypt_imp_Server_msg])));
+                                        Crypt_imp_Server_msg])));
 qed "YM4_imp_Says_Server_A";
 
 
 
 goal thy 
  "!!evs. [| Says A' B {|Crypt {|Agent A, Key K|} (shrK B),              \
 \                       Crypt (Nonce NB) K|} : set_of_list evs;         \
-\           A ~: bad;  B ~: bad;  evs : yahalom |]                      \
-\        ==> Key K ~: analz (sees Enemy evs)";
+\           A ~: lost;  B ~: lost;  evs : yahalom lost |]                      \
+\        ==> Key K ~: analz (sees lost Spy evs)";
 by (fast_tac (!claset addSDs [YM4_imp_Says_Server_A,
-			      Enemy_not_see_encrypted_key]) 1);
+                              Spy_not_see_encrypted_key]) 1);
 qed "B_gets_secure_key";